How to animate particle count?
Animate the children.
As intimated in question, cannot animate the hair particle count. Can however set children and animate the child count.

Sliding the child count viewport display amount, similarly set the render

So for example I want to have like 2000 particles on frame 100 and
want them to reduce to like 200 till frame 300

Example for this case, set particle count to 200, keyframe count as 10 on frame 100, and 1 on frame 300.